Find the Domain 2^(2x)-10*2^x+16=0

Problem

2(2*x)−10⋅2+16=0

Solution

1. Identify the type of expression. The given equation is an exponential equation where the variable x is in the exponent.

2. Determine the domain of the functions involved. The expression consists of exponential terms of the form 2 and 2(2*x)

3. Recall the properties of exponential functions. For any base b>0 the function ƒ(x)=bx is defined for all real numbers.

4. Check for restrictions. There are no denominators containing variables, no square roots of negative numbers, and no logarithms in the original expression.

5. Conclude that since there are no operations that restrict the input x the domain is the set of all real numbers.

Final Answer

Domain=(−∞,∞)

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